Consecutive-k systems correspond to reliability models in which clusters of failed components can cause an overall system failure. The component assignment problem (CAP) aims to determine the optimal arrangement of components with different reliabilities to maximize system reliability. However, there is no algorithm to solve the CAP in threedimensional connected-(1, 1, 2)!-out-of-(n 1 , n 2 , n 3 ):F systems, in which system failure occurs when two adjacent components fail along any axis. To address this problem, we propose an iterated local search algorithm that employs five perturbation strategies to effectively explore the solution space. Computational experiments were conducted on four system sizes, and the results indicate that the choice of perturbation strategy significantly affects solution quality and computational time. Highly disruptive perturbations lead to slow convergence, whereas moderate strategies lead to a better balance between diversification and structure preservation. Furthermore, the experiments revealed that the structure of high-quality solutions and the relative performance of the perturbation methods depend on the odd or even nature of the system dimensions. These findings provide insights into the design of effective search operators for reliability-oriented metaheuristics and have practical implications for optimal deployment of heterogeneous components in three-dimensional sensing and monitoring applications.
Nakamura et al. (Fri,) studied this question.